A1289
Title: Fair logarithmic score for multivariate Gaussian forecasts
Authors: Sandor Baran - University of Debrecen (Hungary) [presenting]
Martin Leutbecher - European Centre for Medium-Range Weather Forecasts (United Kingdom)
Abstract: The verification of multivariate probabilistic forecasts is concerned with evaluating joint probability distributions of vector quantities, such as a weather variable at multiple locations or a wind vector, using scoring rules. The focus is on the strictly proper logarithmic score, which can be applied to ensemble weather forecasts sampled from a specific distribution. Under the assumptions of multivariate normality with mean and covariance matrix given by the ensemble mean and ensemble covariance, respectively, the dependence of the logarithmic score is derived from the ensemble size. It permits estimating the score in the limit of infinite ensemble size from a small ensemble and thus produces a fair logarithmic score. Using ensemble forecasts of vectors consisting of various combinations of upper-air weather variables, the usefulness of the ensemble size adjustments is demonstrated when multivariate normality is only an approximation. It is shown that fair logarithmic scores of ensembles with different cardinalities are very close, in contrast to their unadjusted counterparts, which decrease considerably with ensemble size.
